Nuprl Lemma : oob-getleft_wf
∀[B,A:Type]. ∀[x:{x:one_or_both(A;B)| ↑oob-hasleft(x)} ]. (oob-getleft(x) ∈ A)
Proof
Definitions occuring in Statement :
oob-getleft: oob-getleft(x),
oob-hasleft: oob-hasleft(x),
one_or_both: one_or_both(A;B),
assert: ↑b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
oob-getleft: oob-getleft(x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtype_rel: A ⊆r B,
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
oob-hasleft: oob-hasleft(x),
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
oobleft?_wf,
bool_wf,
eqtt_to_assert,
oobleft-lval_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
pi1_wf_top,
oobboth-bval_wf,
top_wf,
oob-subtype,
equal_wf,
set_wf,
one_or_both_wf,
oob-hasleft_wf,
assert_of_bor,
oobboth?_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
applyEquality,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
axiomEquality,
universeEquality
Latex:
\mforall{}[B,A:Type]. \mforall{}[x:\{x:one\_or\_both(A;B)| \muparrow{}oob-hasleft(x)\} ]. (oob-getleft(x) \mmember{} A)
Date html generated:
2018_05_21-PM-08_00_02
Last ObjectModification:
2017_07_26-PM-05_36_53
Theory : general
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