Nuprl Lemma : assert_functionality_wrt_uiff
∀[u,v:𝔹]. {uiff(↑u;↑v)} supposing u = v
Proof
Definitions occuring in Statement :
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_witness,
assert_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesis,
independent_isectElimination,
equalitySymmetry,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity
Latex:
\mforall{}[u,v:\mBbbB{}]. \{uiff(\muparrow{}u;\muparrow{}v)\} supposing u = v
Date html generated:
2016_05_13-PM-03_56_23
Last ObjectModification:
2015_12_26-AM-10_52_19
Theory : bool_1
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