Nuprl Lemma : node_complete_wf
∀n:node. (node_complete{i:l}(n) ∈ ℙ)
Proof
Definitions occuring in Statement :
node_complete: node_complete{i:l}(n),
node: node,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
node_complete: node_complete{i:l}(n),
prop: ℙ,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
node: node,
pi1: fst(t),
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
pi2: snd(t)
Lemmas referenced :
l_all_wf2,
dl-prop_wf,
l_member_wf,
pi1_wf_top,
list_wf,
istype-void,
dl-localT_wf,
dl-prop-obj_wf,
dl-localF_wf,
node_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
productEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
productElimination,
hypothesisEquality,
lambdaEquality_alt,
independent_pairEquality,
isect_memberEquality_alt,
voidElimination,
universeIsType,
setElimination,
rename,
because_Cache,
applyEquality,
dependent_functionElimination,
inhabitedIsType,
setIsType
Latex:
\mforall{}n:node. (node\_complete\{i:l\}(n) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-09_02_04
Last ObjectModification:
2019_11_27-PM-02_29_16
Theory : dynamic!logic
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