Nuprl Lemma : implies-prop-truncation
∀T:Type. (T ⇒ ⇃(T))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
all: ∀x:A. B[x],
implies: P ⇒ Q,
true: True,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
subtype_quotient,
true_wf,
equiv_rel_true
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesisEquality,
universeEquality,
rename,
introduction,
cut,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesis,
independent_isectElimination
Latex:
\mforall{}T:Type. (T {}\mRightarrow{} \00D9(T))
Date html generated:
2016_05_14-PM-09_37_48
Last ObjectModification:
2015_12_26-PM-09_49_40
Theory : continuity
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