Nuprl Lemma : K_forces_atomic_lemma
∀vars,R,K:Top. (K-forces(K;R(vars)) ~ λi,a. i,a |= R(vars))
Proof
Definitions occuring in Statement :
K-forces: K-forces(K;fmla),
K-sat: i,a |= fmla,
mFOatomic: name(vars),
top: Top,
all: ∀x:A. B[x],
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
K-forces: K-forces(K;fmla),
mFOatomic: name(vars),
mFOL_ind: mFOL_ind
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
inhabitedIsType,
hypothesisEquality,
universeIsType,
introduction,
extract_by_obid,
sqequalRule
Latex:
\mforall{}vars,R,K:Top. (K-forces(K;R(vars)) \msim{} \mlambda{}i,a. i,a |= R(vars))
Date html generated:
2019_10_16-AM-11_45_17
Last ObjectModification:
2018_10_15-PM-06_43_21
Theory : minimal-first-order-logic
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