Nuprl Lemma : assert-pushdown-test
∀C:𝔹. ↑((C ∧b C) ∨bC) supposing ↑(C ∧b C)
Proof
Definitions occuring in Statement :
bor: p ∨bq,
band: p ∧b q,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q),
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
cand: A c∧ B,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
assert: ↑b,
true: True,
bfalse: ff,
false: False
Lemmas referenced :
iff_transitivity,
assert_wf,
bor_wf,
band_wf,
or_wf,
and_wf,
iff_weakening_uiff,
assert_of_bor,
assert_of_band,
bool_cases_sqequal,
assert_witness,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
independent_pairFormation,
orFunctionality,
productElimination,
independent_isectElimination,
inlFormation,
unionElimination,
sqequalRule,
natural_numberEquality,
voidElimination
Latex:
\mforall{}C:\mBbbB{}. \muparrow{}((C \mwedge{}\msubb{} C) \mvee{}\msubb{}C) supposing \muparrow{}(C \mwedge{}\msubb{} C)
Date html generated:
2016_05_13-PM-03_57_44
Last ObjectModification:
2015_12_26-AM-10_51_20
Theory : bool_1
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