Nuprl Lemma : page55'
∀[U:Type]. ∀[P,Q:U ⟶ ℙ]. ∀f:∀x:U. (P[x] ⇒ Q[x]). ∀g:∀x:U. P[x]. ∀x:U. Q[x]
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[U:Type]. \mforall{}[P,Q:U {}\mrightarrow{} \mBbbP{}]. \mforall{}f:\mforall{}x:U. (P[x] {}\mRightarrow{} Q[x]). \mforall{}g:\mforall{}x:U. P[x]. \mforall{}x:U. Q[x]
Date html generated:
2016_05_15-PM-07_42_35
Last ObjectModification:
2015_12_27-AM-11_13_07
Theory : general
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