Nuprl Lemma : iff_weakening_equal
∀[A,B:Type]. {A ⇐⇒ B} supposing A = B ∈ Type
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
independent_pairFormation,
lambdaFormation,
hyp_replacement,
hypothesisEquality,
equalitySymmetry,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality
Latex:
\mforall{}[A,B:Type]. \{A \mLeftarrow{}{}\mRightarrow{} B\} supposing A = B
Date html generated:
2016_05_13-PM-03_07_21
Last ObjectModification:
2016_01_06-PM-05_28_39
Theory : core_2
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